Premiums are slated to rise steeply next year for health plans across the board. Yet almost half of voters who have health coverage under Obamacare say they will keep their current plan through 2016, according to a new Morning Consult online poll.

The findings could be a worrying sign for the Obama administration, which is urging people who buy their insurance on state or federal exchanges to shop around for new plans to avoid premium increases. But the results could also be seen as a positive sign for Obamacare, generally. Half of enrollees are satisfied with their current plan and another one-third are comfortable enough with the online exchanges to look for cheaper coverage, as intended.

“More than half of the 4.17 million people who re-enrolled in coverage during Open Enrollment came back and actively selected a plan and more than half of those consumers selected a new plan,” said Andy Slavitt, Principal Deputy Administrator of CMS. “Based on my experience looking at enrollment trends with employer-sponsored coverage and Medicare, it is clear that Marketplace consumers are more active, engaged, and eager to shop for the coverage that's right for them.”